Transcription of Chapter 2 Graphs - Cornell University
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Chapter 2 Graphs - Cornell University
Chapter 2 GraphsFrom the bookNetworks, Crowds, and Markets: Reasoning about a Highly Connected David Easley and Jon Kleinberg. Cambridge University Press, preprint on-line at this first part of the book we develop some of the basic ideas behind graph theory,the study of network structure. This will allow us to formulate basic network properties in aunifying language. The central definitions here are simple enough that we can describe themrelatively quickly at the outset; following this, we consider some fundamental applicationsof the Basic DefinitionsGraphs: Nodes and a way of specifying relationships among a collec-tion of items. A graph consists of a set of objects, callednodes, with certain pairs of theseobjects connected by links callededges. For example, the graph in Figure (a) consistsof 4 nodes labeledA,B,C, andD, withBconnected to each of the other three nodes byedges, andCandDconnected by an edge as well.
GRAPHS B A C D (a) A graph on 4 nodes. B A C D (b) A directed graph on 4 nodes. Figure 2.1: Two graphs: (a) an undirected graph, and (b) a directed graph. will be undirected unless noted otherwise. Graphs as Models of Networks. Graphs are useful because they serve as mathematical models of network structures.
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